Frequency modulation apparatus and frequency modulation method

ABSTRACT

Disclosed are a frequency modulation apparatus and a frequency modulation method for generating an image clock that is used for turning on/off a laser beam that scans an image bearing member, such as a photosensitive drum. The frequency modulation apparatus divides, into a plurality of segments for each pixel, a main scan line on an image bearing member, and calculates auxiliary clock periods based on a reference clock period and variable-magnification coefficients corresponding to the segments. Then, the frequency modulation apparatus generates image clocks for the respective segments based on an initial predesignated period value and the obtained auxiliary clock periods. Furthermore, the frequency modulation apparatus includes a detecting device for detecting a difference between a reference value stored in a memory and an actual laser irradiation location, and corrects a shift in the laser irradiation location in accordance with the detection results obtained by the detecting device.

BACKGROUND OF THE INVENTION

[0001] 1. Field of the Invention

[0002] The present invention relates to a frequency modulation apparatusand a frequency modulation method for generating an image clock that isused for turning on/off a laser beam that scans an image bearing member,such as a photosensitive drum.

[0003] 2. Related Background Art

[0004] In an electrophotographic image forming apparatus, generally,latent image forming is performed by turning on or off a laser beamemitted by a semiconductor laser and by exposing a photosensitive drumto the laser beam using a polygon mirror, and the image forming isperformed by developing the latent image to obtain a toner image andtransferring the toner image to a recording medium.

[0005] For this image forming apparatus, a constant clock is alwaysemployed as an image clock that is required for a laser controller thatturns on or off a laser beam in accordance with input image data, and asa reference clock that is used as a reference for the generation of theimage clock. The reason for this is as follows. If a reference clock isnot constant, an image clock having a correct frequency can not begenerated, a fluctuation is caused at this frequency, and the ON/OFFtiming for the laser beam is shifted from the proper timing.Accordingly, the dot formation location for a latent image formed on aphotosensitive member is slightly changed, and as a result, imagedistortion, misregistration and uneven coloring occur.

[0006] Further, for the image forming apparatus, a f-θ lens 40 islocated between a polygon mirror 38 and a photosensitive member 42 inFIG. 1. The f-θ lens 40 possesses such optical characteristics as alaser beam condensing function and a distortion aberration correctionfunction for ensuring linearity is maintained for scanning along a timeaxis, and is provided in order to scan a photosensitive member with alaser beam at a uniform speed. Therefore, the characteristics of the f-θlens 40 greatly affect the printing accuracy in the scan direction.

[0007] In FIG. 10, a relationship between a print position and thedistortion rate of the f-θ lens 40. The f-θ lens 40 has the f-θcharacteristic, which is an optical characteristic shown by a curve inFIG. 10, and generally, as it is closer to the end area, the speed ofscanning the photosensitive member 42 is increased, so that scanning ata completely uniform velocity is not obtained. That is, the distortionrate is increased from the center of the f-θ lens 40 (the central printposition) to the end, and this is greatly related to a shift in theprint positions at both ends of an image.

[0008] A detailed explanation for this problem will be described whilereferring to FIG. 11. When a specific pixel at the main scan end isdenoted by Ps(N−1) and the next pixel is denoted by PsN, an interval Dsbetween the pixels at the end areas is represented as

Ds=PsN−Ps(N−1).

[0009] Similarly, when a specific pixel in the scan center area isdenoted by Pc(N−1) and the next pixel is denoted by PcN, a distance Dcbetween these pixels is represented as

Dc=PcN−Pc(N−1).

[0010] Because of the above described characteristic of the f-θ lens 40,Ds>Dc is obtained, i.e., the pixel interval differs depending on thescanning position. As a result, an image is printed while themagnification rate differs, depending on the portions of the image, andan accurate image reproduction is not possible.

[0011] In order to minimize the print position shift that occurs due tothe characteristic of the f-θ lens, conventionally, a frequencymodulation technique is employed to modulate the frequency of an imagewrite clock, and the shift in the print position is correctedelectrically. There are, for example, a method for uniquely changing afrequency for one scan interval and a method for dividing one scaninterval, and for modulating a frequency in an analog manner (e.g.,Japanese Patent Application Laid-Open No. H2-282763).

[0012] However, as is apparent from FIGS. 10 and 11, the characteristicof the f-θ lens is complicated, and the distortion rate is increased,depending on the lens material. Therefore, according to the method usedfor uniquely changing the frequency for one scan interval, and themethod for dividing one scan interval and modulating the frequency in ananalog manner, accuracy can not be expected for the correction of theprint position shift that occurs due to the characteristic of the f-θlens. As a result, the printing quality is deteriorated.

[0013] For a color image forming apparatus, the above described f-θ lens40 is provided for each of the colors Y, M, C and K. Because of thevariations in the characteristics of the individual colors, thelocations at which the photosensitive drum 42 is irradiated is shifted,even for pixels at the same position. As a result, misregistration inimage forming occurs, and the image quality is remarkably deteriorated.

[0014] To resolve this problem, a well known apparatus is provided inJapanese Patent Application Laid-Open No. H9-218370 (Fuji Film). Thisapparatus partially modulates the frequency of an image clock along oneline and ensures that scanning is performed at a uniform speed, so thatany scan speed fluctuation produced by the f-θ characteristic iscanceled.

[0015] However, as is shown in FIG. 15, even for the same lens, the f-θcharacteristic differs for each apparatus due to errors in the size andattachment of the lens, and irradiation location shifts can not beavoided. Expensive lenses are required to reduce the variations inmanufacturing lenses, and complicated operations are required toaccurately position and attach the lenses.

[0016] A method for correcting variations in individual apparatuses isdisclosed in Japanese Patent Application Laid-Open No. H11-198435 (FujiXerox). According to this method, instead of identical frequencies beingmodulated for a plurality of apparatuses, in each apparatus aregistration mark is detected at multiple predetermined locations in themain scan direction, and frequency modulation, based on the detection ofthe distance shifted, is performed to correct for the shifting.According to this method, corrections in consonance with thecharacteristics of the individual apparatuses are enabled and performed.

[0017] However, as is shown in FIG. 12, since the absolute scan positionfor a specific pixel N is the cumulative accumulation from the scanstart position, the positions of pixels 0 to (N−1) must be established,i.e., the pixel clock frequencies up to fn−1 must be determined.Therefore, all the frequency setup values must be used to performcalculations for the individual apparatuses for which readjustments arerequired. And since for these calculations, complicated algorithms andprocedures are required, and since all the setup values must be storedin FIG. 13, an increased memory (RAM) capacity is required.

[0018] Further, as is shown in FIG. 25, the frequency modulationconfiguration of an image forming apparatus constituted by multi-beamlaser comprises: a plurality of setting registers 72, 74 and 76 and aplurality of frequency modulating devices 71, 73 and 75 for generatingimage signal clocks 77, 78 and 79 for a plurality of laser beams. Thesetting registers 72, 74 and 76 hold setup values(variable-magnification coefficients) for one line in the main scandirection of a laser beam, or for the number of segments constitutingthe line. The frequency modulating devices 71, 73 and 75 generate theimage signal clocks 77, 78 and 79 based on a reference clock signalRefclk, which is generated by a reference clock generating unit 70, andthe setup values that are received from the corresponding settingregisters 72, 74 and 76.

[0019] An image forming apparatus constituted by multi-beam lasersrequires setting registers, i.e., correction tables, equivalent innumber to the number of laser beams in order to perform correctionsconsonant with the characteristics of the f-θ lens. That is, a pluralityof correction tables must be prepared in accordance with the locationspassed by the laser beams and the characteristics of the f-θ lens.Therefore, for a plurality of laser beams, it takes time to performcorrections such as the preparation of correction tables, and theoperation is very demanding.

SUMMARY OF THE INVENTION

[0020] It is one object of the present invention to provide a frequencymodulation apparatus that can correct, with high accuracy, a printingratio and that can obtain a superior printing quality.

[0021] To achieve this object, according to one aspect of the presentinvention, a frequency modulation apparatus comprises:

[0022] a segmentalizing device for dividing, into a plurality ofsegments in units of pixel, a main scan line on an image bearing memberscanned by a laser beam;

[0023] an auxiliary clock calculation device for employing a referenceclock period, and variable-magnification coefficients corresponding tothe respective segments, to calculate auxiliary clock periods for therespective segments;

[0024] an image clock generating device for generating image clocks forthe respective segments based on an initial predesignated period valueand the auxiliary clock periods for the respective segments;

[0025] a reference value storing device for storing a reference value;

[0026] a detecting device for detecting a difference between thereference value and an actual laser irradiation location; and

[0027] a correcting device for correcting a shift in the laserirradiation location in accordance with the detection results obtainedby the detecting device.

[0028] With this configuration, a superior printing quality can beobtained that is not affected by the characteristics of an f-θ lens.

[0029] The above and other objects, features and advantages of theinvention will become more apparent from the following detaileddescription taken in conjunction with the accompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

[0030]FIG. 1 a specific diagram showing the arrangement of the opticalscanning unit of an image forming apparatus according to a firstembodiment of the present invention;

[0031]FIG. 2 is a block diagram showing the arrangement of a main scanmagnification correcting circuit according to the first embodiment ofthe invention;

[0032]FIG. 3 is a block diagram showing the arrangement of an imageclock generating unit 17 in FIG. 2;

[0033]FIG. 4 is a graph showing the relationship between segments andthe image clock periods in these segments;

[0034]FIGS. 5A and 5B are graphs in each of which is shown arelationship when the period for the image clock in the segment isvaried at multiple steps;

[0035]FIG. 6 is a diagram for explaining a control method used by themain scan magnification correcting circuit in FIG. 2;

[0036]FIG. 7 is a block diagram showing the internal structure of a mainscan distance dk detecting circuit and a main scan distance dk measuringcircuit in FIG. 2;

[0037]FIG. 8 is a timing chart for the essential block in FIG. 7;

[0038]FIG. 9 is a diagram showing an example printing pattern;

[0039]FIG. 10 is a graph showing an example relationship between printpositions and the distortion rate of an f-θ lens;

[0040]FIG. 11 is a diagram for explaining an f-θ characteristic curveand print locations on a photosensitive drum;

[0041]FIG. 12 is a diagram for explaining the absolute scan position fora pixel N;

[0042]FIG. 13 a diagram showing a conventional example of the storing asetup value for performing readjustment;

[0043]FIG. 14 is a diagram for explaining segments that are divided intoblocks;

[0044]FIG. 15 is a diagram showing the state wherein the f-θcharacteristic curve is shifted;

[0045]FIG. 16 is a diagram for explaining a second embodiment of thepresent invention (one adjusted segment/block);

[0046]FIG. 17 is a diagram for explaining a third embodiment of thepresent invention (multiple adjusted segments/block);

[0047]FIG. 18 is a specific diagram showing the arrangement of amulti-beam optical scan unit provided for an image forming apparatusaccording to a fourth embodiment of the present invention;

[0048]FIG. 19 is a block diagram showing a frequency modulationconfiguration for generating an image clock signal to be supplied to alaser driving circuit in FIG. 18;

[0049]FIG. 20 is a block diagram showing the structures of frequencymodulating devices in FIG. 19;

[0050]FIGS. 21A, 21B, 21C and 21D are diagrams for explaining dataconversion methods used by a register value producing unit;

[0051]FIG. 22 is a specific diagram showing the structure of an f-θ lensmanufactured using multi-shots;

[0052]FIG. 23 is a block diagram showing a frequency modulationconfiguration according to a fifth embodiment of the present invention;

[0053]FIG. 24 is a block diagram showing a frequency modulationconfiguration according to a sixth embodiment of the present invention;and

[0054]FIG. 25 is a block diagram showing a frequency modulationconfiguration for a conventional image forming apparatus constituted bya multi-beam laser.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0055] The present invention will now be described below in detail whilereferring to the accompanying drawings showing preferred embodimentstherefor. In the drawings, elements and parts which are identicalthroughout the views are designated by identical reference numerals, anda duplicate descriptions therefor are omitted.

[0056]FIG. 1 is a specific diagram showing the configuration of theoptical scanning unit of an image forming apparatus according to a firstembodiment of the present invention.

[0057] As is shown in FIG. 1, the optical scanning unit comprises: alaser unit 36 constituted by a semiconductor laser and a collimator lens(not shown), and a laser driving circuit 35 for driving the laser unit36. As control signals for turning on or off a laser beam, a printingpattern signal and an image clock, which will be described later, aretransmitted by a main scan magnification correcting circuit to the laserdriving circuit 35.

[0058] In a non-image area, a laser beam L1 emitted by the laser unit 36is passed through a cylindrical lens 37 and reaches a polygon mirror 38that is rotated at a uniform angular velocity by a scanner motor unit39. The laser beam L1 that has reached the polygon mirror 38 isdeflected by the polygon mirror 38, and the deflected beam then entersan f-θ lens 40. Because of the condensing function and the distortionaberration correction function of the f-θ lens 40, the laser beam isconverted into a laser beam that scans at a uniform speed in a directionperpendicular to the rotation direction of a photosensitive drum 42. Theobtained laser beam is received by a beam detecting sensor 43.

[0059] In an image area, in the same way as the laser beam L1, a laserbeam L2 passes through the cylindrical lens 37, the polygon mirror 38and the f-θ lens 40, and is converted into a laser beam that scans at auniform speed in the direction perpendicular to the rotation directionof the photosensitive drum 42. The obtained laser beam passes throughthe f-θ lens 40, and is reflected by a reflection mirror 41, and thereflected beam is projected onto the photosensitive drum 42. Throughthis beam irradiation, a latent image is formed on the photosensitivedrum 42, and by using toner, is visualized as a toner image. The tonerimage is then transferred and fixed to a recording medium. As a result,an image is formed on the recording medium.

[0060] The main scan magnification correcting circuit will now bedescribed while referring to FIG. 2. FIG. 2 is a block diagram showingthe arrangement of the main scan magnification correcting circuitaccording to the first embodiment of this invention.

[0061] The main scan magnification correcting circuit is a circuit thatmodulates an image clock to correct a printing ratio (a shift in theprint positions) of the main scan line. As is shown in FIG. 2, the mainscan magnification correcting circuit includes a main scan distance dkdetecting circuit 1. The main scan distance dk detecting circuit 1detects, as a main scan distance, a distance between target pixels in areference image that is read by an image reading unit that will bedescribed later, and outputs a main scan distance signal 2 thatrepresents the value of the detected distance. The main scan distancesignal 2 is transmitted to a main scan distance dk measuring circuit 3,which then converts this signal 2 into a main scan distance measurementsignal 4 that is time data. The main scan distance dk detecting circuit1 and the main scan distance dk measuring circuit 3 will be describedlater in detail.

[0062] The main scan distance measurement signal 4 is transmitted to aswitch SW. And the changing of the switch SW is controlled in accordancewith a modulated clock control signal 33 output by an image clockgenerating unit 17, and in accordance with the state of the switch SW,the main scan distance measurement signal 4 is transmitted to either aninitial error ratio γ0 calculating circuit 7 or an error ratio γkcalculating circuit 13.

[0063] The initial error ratio γ0 calculating circuit 7 calculates aratio of a value indicated by the main scan distance measurement signal4 to an initial value 6 that is predesignated for an initial value dsstoring circuit 5, and outputs the obtained ratio as an initial errorratio signal 8. The initial error ratio signal 8 is stored in an initialerror ratio γ0 storing circuit 9.

[0064] The error ratio γk calculating circuit 13 calculates a ratio of avalue indicated by the main scan distance measurement signal 4 to apredetermined value 12 that is predesignated for a predetermined value dstoring circuit 11, and outputs the obtained ratio as an error ratiosignal 14. The error ratio signal 14 is stored in an error ratio γkstoring circuit 15.

[0065] The initial error ratio signal 8, which is stored in the initialerror ratio γ0 storing circuit 9, and the error ratio signal 14, whichis stored in the error ratio γk storing circuit 15, are transmitted tothe image clock generating unit 17. Based on the value indicated by theinitial error ratio signal 8 or the value indicated by the error ratiosignal 14, the image clock generating unit 17 performs frequencymodulation for a predesignated image clock, and outputs the obtainedclock as an image clock 18. Further, the image clock generating unit 17also outputs a printing pattern control signal 19 indicating an imagethat has been read by the image reading unit.

[0066] (Image Clock Generating Unit)

[0067] The arrangement of the image clock generating unit 17 will now bedescribed while referring to FIGS. 3 and 4. FIG. 3 is a block diagramshowing the arrangement of the image clock generating unit 17 in FIG. 2,and FIG. 4 is a graph showing a relationship between a segment and theperiod of the image clock 18 in the segment.

[0068] As is shown in FIG. 3, the image clock generating unit 17includes a reference clock generating unit 20, a variable-magnificationcoefficient setting register 22, an auxiliary pixel producing circuit24, an initial period setting register 26, a modulated clock controlcircuit 30, a number of pixels setting register 31 and a modulated clockgenerating circuit 28.

[0069] The reference clock generating unit 20 generates a referenceclock signal 21 having an arbitrary frequency. In accordance with anerror ratio γk, a variable-magnification coefficient 23 is designated tovary the period ratio of the reference clock signal 21, and is held inthe variable-magnification coefficient setting register 22.

[0070] The auxiliary pixel producing circuit 24 produces an auxiliarypixel period 25 based on the reference clock signal 21 and thevariable-magnification coefficient 23. When the period of the referenceclock signal 21 is, for example, τref, the variable-magnificationcoefficient 23 is αk and the auxiliary pixel period 25 is Δτ. Δτ isrepresented by the following equation (1).

Δτ=αk·τref  (1)

[0071] wherein the variable-magnification coefficient 23 (αk) is set tosuch a value that the auxiliary pixel period 25 (Δτ) is sufficientlyshorter than the period of the image clock 18.

[0072] In accordance with an initial error ratio γ0, an initial value 27(τvdo) is set for the period of the image clock 18 output by the imageclock generating unit 17, and is held in the initial period settingregister 26.

[0073] The modulated clock control circuit 30 divides one line in themain scan direction into a plurality of segments, each of which isconstituted by an arbitrary number of pixels. The modulated clockcontrol circuit 30 controls the image clock period between the segments,or within each segment. The number of pixels in a segment is designateda pixel count setup value 32 stored in the number of pixels settingregister 31. Either a different number of pixels or the same number ofpixels may be employed for the individual segments.

[0074] The detailed operation of the modulated clock control circuit 30will now be described. When the modulated clock control circuit 30receives, from the beam detecting sensor 43, a beam detection signal (BDsignal) 29 indicating a printing reference position, the modulated clockcontrol circuit 30 generates the modulated clock control signal 33 forthe first segment (segment 0), and outputs this signal 33 to themodulated clock generating circuit 28. Upon receiving the modulatedclock control signal 33, the modulated clock generating circuit 28outputs the image clock 18 having the initial period 27 (τvdo) that isstored in the initial period setting register 26.

[0075] The modulated clock control circuit 30 then generates themodulated clock control signal 33 for the next segment (segment 1), andoutputs this signal 33 to the modulated clock generating circuit 28.Upon receiving the modulated clock control signal 33, the modulatedclock generating circuit 28 employs the auxiliary pixel period 25 (Δτ)and the initial period 27 (τvdo) to generate, as the image clock 18, amodulated clock signal ΔT1 that has a period represented by thefollowing equation (2).

ΔT 1=τvdo+α1·τref  (2)

[0076] wherein α1 denotes a variable-magnification coefficient for thesegment 1.

[0077] Further, the modulated clock control circuit 33 generates themodulated clock control signal 33 for the next segment (segment 2), andoutputs this signal 33 to the modulated clock generating circuit 28.Upon receiving the modulated clock control signal 33, the modulatedclock generating circuit 28 employs the auxiliary pixel period 25 andthe initial period 27 to generate, as the image clock 18, a modulatedclock signal ΔT2 that has a period represented by the following equation(3).

ΔT 2=τvdo+α1·τref+α2·τref  (3)

[0078] wherein α2 denotes a variable-magnification coefficient for thesegment 2.

[0079] In the same manner, modulated clock control signal 33 isgenerated for segments following the segment 2 and is output as theimage clock 18.

[0080] As is described above, under the control of the modulated clockcontrol circuit 30, the image clock 18 having a plurality of periods inone scan line is output from the modulated clock generating circuit 28.

[0081] Furthermore, at least one of the points whereat the segments arechanged, the modulated clock control circuit 30 selects the last pixelin the preceding segment, or an arbitrary number of pixels proceedingfrom the last pixel, and generates the printing pattern control signal19 that includes the selected pixels. It should be noted, however, thatthe location whereat the segment switching pattern is output isidentical for each line.

[0082] According to the above described control method, one scan line isdivided into a plurality of segments, and the constant image clock 18 isgenerated for each segment. However, frequency modulation of the imageclock may be performed for each segment.

[0083] While referring to FIGS. 5A and 5B, an explanation will now begiven for a segment period control method employed when the frequencymodulation for the image clock is performed in the segment. FIGS. 5A and5B are graphs in each of which is shown a relationship when the periodfor the image clock 18 in the segment is varied at multiple steps.

[0084] (1) Case wherein the initial segment (segment 0) is varied

[0085] When the frequency of the image clock 18 is varied beginning atthe initial segment (segment 0), and when, as is shown in FIG. 5A, theinitial period is τvdo, the number of pixels for one segment is n, thevariable-magnification coefficient (segment 0) is α1 and the referenceclock period is τref. A period Δτa for one pixel in the segment 0 andthe total period ΔT0 for the segment 0 are represented by the followingequations (4) and (5).

Δτa=(α1·τref)/n  (4) $\begin{matrix}\begin{matrix}{{\Delta \quad {T0}} = {{\tau \quad {vdo}} + {\left\{ {n \cdot {\left( {n + 1} \right)/2}} \right\} \cdot \left\{ {\left( {{{\alpha 1} \cdot \tau}\quad {ref}} \right)/n} \right\}}}} \\{= {{\tau \quad {vdo}} + \left\{ {{\left( {n + 1} \right)/2} \cdot \left( {{{\alpha 1} \cdot \tau}\quad {ref}} \right)} \right\}}}\end{matrix} & (5)\end{matrix}$

[0086] (2) Case wherein the initial segment (segment 0) is fixed

[0087] When the frequency of the image clock 18 for the initial segment(segment 0) is fixed and the frequencies of the image clocks 18 for thesucceeding segments are varied, the total period for the segment 0, ΔT0,shown in FIG. 5B, is represented by the following equation (6).

ΔT 0=n·τvdo  (6)

[0088] Whereas, for the next segment of the initial segment, i.e., thesegment 1, when the variable-magnification coefficient (segment 1) is α2and the reference clock period is τref, a period Δτb for one pixel inthe segment 1 and the total period ΔT1 for the segment 1 are representedby the following equations (7) and (8).

Δτb=(α2·τref)/n  (7) $\begin{matrix}\begin{matrix}{{\Delta \quad {T1}} = {{\tau \quad {vdo}} + {\left\{ {n \cdot {\left( {n + 1} \right)/2}} \right\} \cdot \left\{ {\left( {{{\alpha 2} \cdot \tau}\quad {ref}} \right)/n} \right\}}}} \\{= {{\tau \quad {vdo}} + {\left\{ {\left( {n + 1} \right)/2} \right\} \cdot \left( {{{\alpha 2} \cdot \tau}\quad {ref}} \right)}}}\end{matrix} & (8)\end{matrix}$

[0089] For the following segments, a period Δτb for one pixel and thetotal period ΔTn (n≧2) can be represented using the same equations.

[0090] As is apparent from FIGS. 5A and 5B, either when the frequency ofthe image clock 18 is varied beginning at the initial segment (segment0), or when the frequency of the image clock 18 for the initial segment(segment 0) and the frequencies of the image clocks 18 for thesucceeding segments are changed, continuity at the segment switchingpositions can be maintained.

[0091] While referring to FIG. 6, an explanation will now be given for amethod for calculating the initial error ratio γ0 and the error ratioγk, and a method for correcting the initial period 27 and thevariable-magnification coefficient 23 in accordance with these ratios.FIG. 6 is a diagram for explaining a control method employed by the mainscan magnification correcting circuit in FIG. 2.

[0092] A value corresponding to the initial error ratio γ0 and a valuecorresponding to the error ratio γk are respectively stored in theinitial period setting register 26 and the variable-magnificationcoefficient setting register 22, and based on these values, the imageclock 18 is generated. The initial error ratio γ0 is a ratio of adistance (the length of the segment 0) from the printing referenceposition, which is determined based on the BD signal 29, to the actualprint position of the first pixel, to a distance (the length of thesegment 0) from the printing reference position to the ideal printposition of the first pixel. The error ratio γk is a ratio of a distance(the length of the segment 1, . . . ) from the actual print position ofa specific pixel to the actual print position of the next pixel, to adistance (the length of the segment 1, . . . ) from the ideal printposition of the specific pixel to the ideal print position for the nextpixel.

[0093] The actual print position is the print position of a pixel when,based on a predetermined image clock 18, a printing pattern is printedin accordance with the printing pattern control signal 19 setting theprinting of one pixel for each segment. This print position is obtainedby reading the printing pattern. The processing performed to detect theactual print position will be described later.

[0094] The printing pattern is formed of one dot or a plurality of dotslocated at a position preceding or following the switching of thesegments. For example, the segment 0 of the printing pattern is formedof the last one dot or last multiple dots in the interval for thesegment 0. The segment 1 of the printing pattern is formed of the firstdot or first multiple dots in the interval for the segment 1, or may beformed of multiple dots that extend from the last portion of the segment0 interval to the first portion of the segment 1 interval. When thenumber of segments is m and the number of patterns to be printed is k,2≧k≧m≧256 relationship is established, and printing may not necessarilybe performed where the segments are switched. Further, the image clockfor printing in the segment 0 interval is T0=τvdo and the image clockfor printing in the segment 1 interval is T1=α1·τref.

[0095] On the other hand, the ideal print position is a pixel positionfor the printing pattern that is theoretically obtained in advance whiletaking into account the expected optical characteristic of the f-θ lensand the image clock period. A distance (theoretical value) ds from theprinting reference position to the ideal print position for the firstpixel is stored as the initial value 6 in the initial value ds storingcircuit 5. A distance (theoretical value) d from the ideal printposition for a specific pixel to the ideal print position for the nextpixel is stored as the initial value 12 in the predetermined value dstoring circuit 11.

[0096] When S denotes the initial period for the initial segment and S′denotes a corrected initial period, and when ds′ denotes a distance fromthe printing reference position to the actual print position of thefirst pixel, the initial error ratio γ0 is represented as ds′/ds, andthe following equation (9) is established. $\begin{matrix}\begin{matrix}{S^{\prime} = {S \cdot \left( {{ds}^{\prime}/{ds}} \right)}} \\{= {{\gamma 0} \cdot S}}\end{matrix} & (9)\end{matrix}$

[0097] Therefore, in accordance with equation (9), the initial period(theoretical value) stored in advance in the initial period settingregister 26 is corrected to the period S′ consonant with the initialerror ratio γ0.

[0098] For the ideal print position, when n denotes the number of pixelsconstituting each segment (each segment following the segment 1), tdenotes a period for each segment and Ddpi denotes a resolution (printwidth), equation (10) is established.

t=n·τvdo

d=n/Ddpi  (10)

[0099] wherein τvdo is an image clock period.

[0100] Similarly, for the actual print position, when τseg1 denotes animage clock period for the segment 1 and Ddpi1′ denotes the actualresolution, equation (11) is established.

t=n·τseg 1

d 1=n/Ddpi 1′  (11)

[0101] Because of the relationship between the ideal print position d,which is stored for the segment 1 in the predetermined value d storingcircuit 11, and the actual print position d1 (the main scan distancemeasurement signal 4), which is obtained by the main scan distance dkmeasuring circuit 3, the error ratio γ1 is represented as d1/d, andequation (12) is obtained.

d:d 1=n/Ddpi:n/Ddpi 1′=n·τvdo:n·τseg 1

τseg 1=τvdo·(d1/d)

τseg 1=γ1·τvdo  (12)

[0102] The auxiliary pixel period T1 constituting the segment 1 isT1=τref·α1, based on the reference clock period τref and thevariable-magnification coefficient α, and a correctedvariable-magnification coefficient α1′ is acquired by equation (13).

τseg 1=τref·α1′=γ1τvdo

α1′=γ1·(τvdo/τref)  (13)

[0103] Similarly, when the error ratio γ2 is represented as d2/d basedon the relationship between the ideal print position d and the actualprint position d2 for the segment 2, the auxiliary pixel period T2constituting the segment 2 is T2=τref·α2, wherein thevariable-magnification coefficient is α2. A correctedvariable-magnification coefficient α2′ is acquired by equation (14).

τseg 2=τref·α2′=τ2·τvdo

α2′=γ2·(τvdo/τref)  (14)

[0104] In this manner, in accordance with equations (13) and (14), thevariable-magnification coefficients (theoretical values: α1 and α2)stored in advance in the variable-magnification setting register 22 arecorrected to obtain variable-magnification coefficients (α1′ and α2′)consonant with the error ratios γk (γ1 and γ2).

[0105] The processing for detecting the actual print position will nowbe described while referring to FIGS. 7 to 9. FIG. 7 is a block diagramshowing the internal structure for the main scan distance dk detectingcircuit 1 and the main scan distance dk measuring circuit 3 in FIG. 2.FIG. 8 is a timing chart for the essential block in FIG. 7, and FIG. 9is a diagram showing an example print pattern.

[0106] As is shown in FIG. 7, the main scan distance dk detectingcircuit 1 includes an image reading unit 45, which is a reader scanner,and a comparator 49 and a threshold voltage Vth generating unit 48.

[0107] The main scan distance dk measuring circuit 3 includes an ANDcircuit 50, a counter clock generator CLK 52, a counter 53, an averagingcircuit 55, a main scan period storing circuit 57 and an initial periodcorrecting circuit 58.

[0108] When the main scan distance dk detecting circuit 1 reads, forexample, a print pattern in FIG. 9 to detect the actual print position,first, the image reading unit 45 outputs, as shown in FIG. 8, a startpulse (START PLS) 46, which is a scan start signal to be output for eachmain scan. An image read output 47 is transmitted from the image readingunit 45 to the comparator 49. The comparator 49 compares the image readoutput 47 with a threshold voltage Vth received from the thresholdvoltage Vth generator 48, and binarizes the comparison results. Theobtained binary signal is transmitted as the main scan distance signal 2to the main scan distance dk measuring circuit 3.

[0109] In the main scan distance dk measuring circuit 3, the main scandistance signal 2 and the start pulse (START PLS) 46 are received by theAND circuit 50. The AND circuit 50 transmits a clear signal (clr signal)51 to the counter 53 each time the main scan distance signal 2 at levelH or the start pulse (START PLS) 46 is received. Until the next clearsignal clr is transmitted by the AND circuit 50, the counter 53 counts acounter clock generated by the CLK 52 and outputs a count value 54. Forexample, the count value from the input of the start pulse (START PLS)to the input of the main scan distance signal 2 at level H is theinitial period count value that corresponds to a distance from theprinting reference position to the actual print position of the firstpixel, i.e., the length of the segment 0 in the main scan direction. Thecount value 54 of the counter 53 is transmitted to the averaging circuit55, and the averaging circuit 55 obtains the average for the individualcount values 54 obtained for the individual main scans until the mainscan reading has been repeated a predetermined number of times, i.e.,the start pulse (START PLS) 46 has been received a predetermined numberof times. The averaging process performed by the averaging circuit 55 isperformed in order to suppress an error in the image reading unit 45,and arbitrary times may be employed for the performance of the averagingprocess. The averaged count values 56 are stored in the main scan periodstoring circuit 57.

[0110] Among the averaged count values 56 stored in the main scan periodstoring circuit 57, the initial period count value is corrected by theinitial period correcting circuit 58 in order to correct the printingtiming relative to the scan start timing for the image reading unit 45.This is because there is a phase difference between the start pulse(START PLS) 46 used by the main scan period dk measuring circuit 3 andthe BD signal 29 used to determine the printing position.

[0111] The averaged count value 56 stored in the main scan periodstoring circuit 57 is output to the switch SW as the main scan distancemeasurement signal 4. When the main scan distance measurement signal 4is for the initial period, i.e., the segment 0 is transmitted to theswitch SW, the switch SW is changed in accordance with the modulatedclock control signal 33 received from the image clock generating unit17, so that the main scan distance measurement signal 4 for the initialperiod is transmitted to the initial error ratio γ0 calculating circuit7. When the main scan distance measurement signal 4 for another segmentis transmitted to the switch SW, the switch SW is changed in accordancewith the modulated clock control signal 33 received from the image clockgenerating unit 17, so that the main scan distance measurement signal 4for this segment is transmitted to the error ratio γk calculatingcircuit 13.

[0112] As is described above, according to this embodiment, a referenceimage (shown in FIG. 9) is read, and an inter-pixel distance (the mainscan distance measurement signal 4) is measured that corresponds to eachof the segments of the reference image. The error ratio γk of eachobtained inter-pixel distance to the ideal inter-pixel distance iscalculated, and the variable-magnification coefficient αk, whichcorresponds to the obtained error ratio γk, is changed. Therefore, theprint ratio can be accurately corrected, and a superior printing qualitycan be obtained.

[0113] All or part of the blocks constituting the main scanmagnification correcting circuit (except for the image reading unit 45of the main scan distance dk detecting circuit 1) may be provided as anASIC or another integrated circuit.

[0114] (Explanation For Re-correction)

[0115] As is shown in FIG. 14, the positions of output print patternsL1, L2, L3, . . . are detected (a BD sensor is provided at the printpattern irradiation position, and as an optical sensor or a CIS arrangedin the apparatus is employed to read the print pattern, or the printedpaper is read by a scanner), and a distance between the actual printposition and the ideal position is obtained. Then, only the re-correctedvalue for a predetermined segment of each block is stored in the RAM,and the values set for the other segments are stored as fixed values ina non-rewritable ROM.

[0116] A second embodiment for performing re-correction will now bedescribed while referring to FIG. 16. Actually, a block is formed of 100or more segments. However, to simplify the explanation, one block isformed of twelve segments. The twelve segments are divided every foursegments to form groups, and print patterns L1 r, L2 r and L3 r areprinted on paper and read by a scanner. Based on the obtained imagedata, the positions of the print patterns are detected while referringto the reference position (main scan start position), and shiftdistances h1, h2 and h3 from ideal values L1, L2 and L3 are obtained.Further, a shift distance (or shift amount) hn−n (n−1) for each block iscalculated. In the example in FIG. 16, the following distances areobtained.

[0117] shift distance in block 1=h1

[0118] shift distance in block 2=h2−h1

[0119] shift distance in block 3=h3−h2

[0120] By using the shift distance (or shift amount) for each block andthe image clock modulation method described above, modulationcoefficients are re-calculated only for adjustment target segments 4, 8and 12, which are last segments of the individual blocks, and are againstored in the RAM. When the scan velocities of the segments are V4, V8and V12, the frequencies before adjustment are f4, f8 and f12, and thefrequencies after adjustment are f′4, f′8 and f′12,

f′4=f 4+V 4/h1

f′8=f 8+V 8/(h2−h1)

f′12=f 12+V 12/(h3−h2)

[0121] Thereafter, the adjusted values are employed for the frequencymodulation. While the full capacity of the RAM used to store the setupvalues for all twelve segments is required, according to the secondembodiment, the memory capacity can be reduced to ¼ to store the setupvalues for only three segments. Furthermore, since the frequencies canbe independently adjusted for the individual blocks, a complicatedalgorithm is also not required.

[0122] Further, for the position detection in this example, the printpattern is output to paper; however, a print pattern formed on thephotosensitive drum may be detected. In addition, the number of segmentsfor each block may not be equal, e.g., block 1: segments 1 to 6, block2: segments 7 and 8, and block 3: segments 9 to 12.

[0123] The re-correction process for a third embodiment will now bedescribed while referring to FIG. 17. The arrangement of the blocks andthe calculation of the shift distance are performed in the same manneras in the first embodiment.

[0124] shift distance in block 1=h1

[0125] shift distance in block 2=h2−h1

[0126] shift distance in block 3=h3−h2

[0127] In this embodiment, for each block, there are a plurality ofsegments to be adjusted. In FIG. 17, two segments in each block are tobe adjusted as follows.

[0128] target segments in block 1:3 and 4

[0129] target segments in block 2:7 and 8

[0130] target segments in block 3:11 and 12

[0131] The following two methods are used to calculate the adjustmentvalues.

[0132] 2-1) Calculation of different values for individual segments tobe adjusted

[0133] When the scan velocities of the segments are V3, V4, V7, V8, V11and V12, and the frequencies before adjustment are f3, f4, f7, f8, f11and f12 and the frequencies after re-adjustment are f′3, f′4, f′7, f′8,f′11 and f′12, the adjusted frequencies are obtained as follows by anequal distribution of the shift distances.

f′3=f 3+V 3/(h½)

f′4=f 4+V 4/(h{fraction (1/2)})

f′7=f 7+V 7/{(h2−h1)/2}

f′8=f 8+V 8/{(h2−h1)/2}

f′11=f 11+V 11/{(h3−h2)/2}

f′12=f 12+V 12/{(h3−h2)/2}

[0134] According to this method, the amount of absorption of the shiftdistance after correction can be dispersed.

[0135] 2-2) Calculation of the same value for adjustment target segmentsin each block

[0136] According to this method, the same value is set for the targetsegments in each block. That is, f3=f4 and f7=f8 and f11=f12, and thefrequencies after adjustment can be obtained by averaging the scanvelocities.

f′3=f′4=f 3+{(V 3+V 4)/2}/h1

f′7=f′8=f 7+{(V 7+V 8)/2}/{(h2−h1)/2}

f′11=f′12=f 11+{(V 11+V 12)/2}/{(h3−h2)/2}

[0137] According to this method, the capacity of the RAM can be reducedeven more, while the shift distance can be dispersed.

[0138] According to the present invention, the variation unique to thef-θ lens can be re-corrected. Further, since only a small number ofsegments must be readjusted, the processing and the algorithm can besimplified by employing a memory having a small capacity.

[0139]FIG. 18 is a specific diagram showing the arrangement of amulti-beam optical scan unit according to a fourth embodiment. In thefollowing explanation, two beams are employed.

[0140] As is shown in FIG. 18, the optical scan unit includes a laserdriving circuit 35 and a laser unit 36 driven by the laser drivingcircuit 35. The laser unit 36 is constituted by a semiconductor laser(not shown) that can emit two laser beams at the same time and acollimator lens (also not shown). The laser driving circuit 35 receivesan image signal and an image clock that will be described later, anddrives the semiconductor laser based on the image signal and the imageclock.

[0141] In a non-image area, two laser beams L1 emitted by a laser unit36 pass through a cylindrical lens 37 and reach a polygon mirror 38 thatis rotated at a uniform angular velocity by a scanner motor unit 39. Thelaser beams that reach the polygon mirror 38 are deflected by thepolygon mirror 38, and the deflected laser beams L1 then enter an f-θlens 40. The laser beams L1 that have entered the f-θ lens 40 areconverted into laser beams that scan at a uniform speed in the directionperpendicular to the rotation direction of a photosensitive drum 42. Theobtained laser beams L1 are received by a beam detecting sensor (BDsensor) 43.

[0142] In an image area, in addition to the laser beams L1, two laserbeams L2 enter the f-θ lens 40 and are converted into laser beams thatscan at a uniform speed in the direction perpendicular to the rotationdirection of the photosensitive drum 42. The obtained laser beams L2 arereflected by a reflection mirror 41, and the reflected beams areprojected onto the photosensitive drum 42. Through the irradiation bythese beams, an electrostatic latent image is formed on thephotosensitive drum 42, and a toner image is visualized by theapplication of toner. The toner image is then transferred and fixed to arecording medium. Through this processing sequence, an image is formedon the recording medium, and the recording medium is thereafterdischarged outside the apparatus.

[0143] A frequency control device for generating an image clock signalto be supplied to the laser driving circuit 35 will now be describedwhile referring to FIG. 19. FIG. 19 is a block diagram showing afrequency modulation configuration for generating an image clock signalto be supplied to the laser driving circuit 35 in FIG. 18. In thisexplanation, a modulation frequency configuration for generating imageclock signals for multi-beams (two beams) is employed.

[0144] As is shown in FIG. 19, the frequency modulation configurationfor this embodiment includes two setting registers 112 and 114 and twofrequency modulating devices 111 and 113 in order to generate imageclock signals 116, 117 in consonance with two laser beams. The settingregisters 112 and 114 are provided at a preceding stage, and transmit,to variable-magnification coefficient setting registers 51 that areprovided for the frequency modulation devices 111 and 113 and that willbe described later, setup values (variable-magnification coefficients)for one line in the main scan direction, or for the number of segmentsin the line. The frequency modulating devices 111 and 113 generate imageclocks 116 and 117 based on a reference clock signal Refclk generated bya reference clock generating unit 20, and the setup values(variable-magnification coefficients) received from the correspondingsetting registers 112 and 114. The detailed structures and theoperations of the frequency modulating devices 111 and 113 will bedescribed later.

[0145] A reference table for a first laser beam is held in the settingregister 112. As will be described later, variable-magnificationcoefficients, which are multipliers for varying the period ratio for areference clock signal 21, are entered in this reference table. Asub-table for a second laser beam is held in the setting register 114,and values entered to this sub-table are those that are generated by aregister value producing unit 115 based on the value in the referencetable stored in the setting register 112 and a predesignated correctioncoefficient N.

[0146] The register value producing unit 115 employs a predetermineddata conversion method for preparing the sub-table, but not thereference table. The data conversion method will now be described whilereferring to FIGS. 21A to 21D. FIGS. 21A to 21D are diagrams forexplaining data conversion methods used by the register value producingunit 115.

[0147] There are four predetermined data conversion methods used by theregister value producing unit 115 to generate a sub-table. When asub-table can not be generated by one of the conversion methods based onthe value of the reference value and the predesignated correctioncoefficient N, some of these conversion methods are jointly employed toperform data conversion.

[0148] Specifically, a first conversion method is a method for adding apredetermined value corresponding to the correction coefficient N to thevariable-magnification coefficient of the reference table, or forsubtracting the predetermined value from the variable-magnificationcoefficient (see FIG. 21A). A second conversion method is a method formultiplying the variable-magnification coefficient of the referencetable by a predetermined value corresponding to the correctioncoefficient N (see FIG. 21B). A third conversion method is a method forshifting the variable-magnification coefficient of the reference tableto the right or left, in the main scan direction, by a distanceequivalent to a predetermined value corresponding to the correctioncoefficient N (see FIG. 21C). A fourth conversion method is a methodwhereby, in consonance with the correction coefficient N, thevariable-magnification coefficient in the reference table is adjusted inthe direction leading toward a correction position, centering on themiddle of the f-θ lens (see FIG. 21D).

[0149] A feature of the frequency characteristic is that among the samelenses a similar conversion method is employed that is based on thereference table.

[0150] The structure for the frequency modulating devices 111 and 113will now be described while referring to FIG. 20. FIG. 20 is a blockdrawing showing the structure for the frequency modulating devices 111and 113 in FIG. 19. Since the frequency modulating devices 111 and 113have the same structure, only the structure for the frequency modulatingdevice 111 will be explained.

[0151] The frequency modulating device 111 performs frequency modulationfor a predesignated image clock signal. The frequency modulating device111 includes a reference clock generating unit 20, avariable-magnification coefficient setting register 22, an auxiliarypixel producing circuit 24, an initial period setting register 26, amodulated clock control circuit 30, a number of pixels setting register31 and a modulated clock generating circuit 28.

[0152] The reference clock generating unit 20 generates a referenceclock signal 21 having an arbitrary frequency. A variable-magnificationcoefficient 23, used to vary the period ratio for the reference clocksignal 21, is held in the variable-magnification coefficient settingregister 22.

[0153] The auxiliary pixel producing circuit 24 produces an auxiliarypixel period 25 based on the reference clock signal 21 and thevariable-magnification coefficient 23. When the period for the referenceclock signal 21 is, for example, τref, the variable-magnificationcoefficient 23 is αk and the auxiliary pixel period 25 is Δτ. Δτ isrepresented by the following equation (1).

Δτ=αk·τref  (1)

[0154] wherein the variable-magnification coefficient 23 (αk) is set tosuch a value that the auxiliary pixel period 25 (Δτ) is sufficientlyshorter than the period for an image clock 18 (corresponding to theimage clock 16 or 17 in FIG. 2).

[0155] An initial value 27 (τvdo) for the period for the image clock 18(corresponding to the image clock 16 or 17 in FIG. 2) is held in theinitial period setting register 26.

[0156] The modulated clock control circuit 30 divides one line in themain scan direction into a plurality of segments each of which isconstituted by an arbitrary number of pixels. The modulated clockcontrol circuit 30 controls the image clock period between the segments,or within each segment. The number of pixels in the segment isdesignated as a pixel count setup value 32 stored in the number ofpixels setting register 31. A different number of pixels or the samenumber of pixels may be employed for the individual segments.

[0157] Since the operation of the modulated clock control circuit 30 isthe same as that in FIGS. 5A and 5B, no detailed explanation for thiswill be given.

[0158] Under the control of the modulated clock control circuit 30, theimage clock 18 having a plurality of periods within one scan line isoutput by the modulated clock producing circuit 28.

[0159] As is described above, according to this embodiment, for eachlaser beam, the main scan line is divided into a plurality of segments,and for each segment, the frequency of an image clock is changed basedon the value in the reference table or the sub-table. Since thefrequency modulation for the image clock is performed in this manner,the misregistration and positioning shift caused by a color imageforming apparatus can be suppressed. As a result, a high quality colorimage can be output.

[0160] Further, in accordance with the characteristic f-θ lens 40, oneor some of the four data conversion methods, i.e., addition andsubtraction, multiplication, shifting of a correction position and themagnification adjustment performed for a correction position, centeringon the middle of the lens, are employed, and a sub-table (correctiontable) for the second beam is generated based on the reference table forthe first beam. Therefore, the correction operation can be simplified.

[0161] A fifth embodiment of the present invention will now be describedwhile referring to FIGS. 22 and 23. FIG. 22 is a specific diagramshowing the structure of an f-θ lens by multi-shots, and FIG. 23 is ablock diagram showing a frequency modulation configuration according tothe fifth embodiment of the invention. In FIG. 23, the same referencenumerals are used to denote blocks having the same functions as theblocks in FIG. 19, and no explanation for them will be given.

[0162] Generally, a lens having superior accuracy can be generated usingglass, but glass is expensive. On the other hand, a lens made of plasticis appropriate for practical use, even though the accuracy is lowered,because plastic is less expensive than glass. Therefore, as is shown inFIG. 22, the f-θ lens tends to be manufactured using a plurality ofmolds N-1 to N-8 (multi-shots). When the f-θ lens is produced bymulti-shots, the rough characteristic of the f-θ lens can be obtainedand managed based on the mold number. In this embodiment, this advantageis employed.

[0163] In this embodiment, as is shown in FIG. 23, correctioncoefficients corresponding to the mold numbers N-1 to N-8 in FIG. 22 arestored in a correction coefficient register 118. Among the correctioncoefficients stored in the correction coefficient register 118, acorrection coefficient corresponding to a mold number is selected by acorrection coefficient selecting unit 119, and is transmitted to aregister value producing unit 115. Therefore, a correction table for asecond beam can be easily prepared in consonance with a mold, and animage clock 117 is generated by using the correction table.

[0164] A sixth embodiment of the present invention will now be describedwhile referring to FIG. 24. FIG. 24 is a block diagram showing afrequency modulation configuration according to the sixth embodiment ofthis invention. The same reference numerals are used to denote blockshaving the same functions as the blocks in FIG. 2, and no explanationfor them will be given.

[0165] While in the fifth embodiment a correction coefficient isselected in consonance with a mold (a multi-shot), in this embodiment,reference tables used to perform corrections in consonance with the f-θcharacteristics for a first beam are managed for the individual moldnumbers, and a reference table is selected in accordance with a moldnumber.

[0166] That is, in this embodiment, as is shown in FIG. 24, referencetables for individual molds are stored in a reference table register120, and a reference table corresponding to a mold number is selected bya reference table selecting unit 121. Therefore, the correctionoperation consonant with the f-θ characteristics of a first beam can besimplified.

[0167] In the fifth embodiment and the sixth embodiment, an explanationhas been given for the method whereby the mold for the multi-shot lensis employed to correct the image clock in consonance with thecharacteristics of the f-θ lens. It is also very effective when thesetwo methods are employed together.

[0168] The configuration including all the blocks constituting thefrequency modulating devices, or the configuration including a part ofthese blocks, or the configuration including blocks on in the peripherymay be provided as an ASIC or another integrated circuit.

What is claimed is:
 1. A frequency modulation apparatus comprising: asegmentalizing device for dividing, into a plurality of segments inunits of pixel, a main scan line on an image bearing member scanned by alaser beam; an auxiliary clock calculation device for employing areference clock period, and variable-magnification coefficientscorresponding to the respective segments, to calculate auxiliary clockperiods for the respective segments; an image clock generating devicefor generating image clocks for the respective segments based on aninitial predesignated period value and the auxiliary clock periods forthe respective segments; a reference value storing device for storing areference value; a detecting device for detecting a difference betweenthe reference value and an actual laser irradiation location; and acorrecting device for correcting a shift in the laser irradiationlocation in accordance with the detection results obtained by thedetecting device.
 2. A frequency modulation apparatus according to claim1, wherein the detecting device includes a scan distance measuringdevice for reading a reference image, and measuring a distance betweentarget images that correspond to the segment in the reference image thathas been read, and an error ratio calculating device for calculating anerror ratio of the reference value to the obtained distance between thetarget images; and wherein the correcting device includes avariable-magnification coefficient changing device for, in accordancewith the obtained error ratio, changing a variable-magnificationcoefficient of the corresponding segment.
 3. A frequency modulationapparatus according to claim 1, further comprising: an initial periodchanging device for changing the initial period value.
 4. An imageforming apparatus wherein the frequency modulation apparatus accordingto claim 1 is provided.
 5. A frequency modulation apparatus according toclaim 1, wherein the detecting device separates the segments into blocksof continuous segments, and detects a shift between a laser irradiationposition based on a value predesignated for each of the blocks and anactual laser irradiation position; and wherein, in accordance with thedetection results obtained by the detecting device, the correctingdevice controls a pixel period of the segment, and corrects the shift ofthe laser irradiation position.
 6. A frequency modulation apparatusaccording to claim 5, wherein segment(s) fewer than the segmentsconstituting each of the blocks are defined as segment(s) to beadjusted; and wherein the correcting device controls the pixel periodfor the segment to be adjusted, and corrects an error for the laserirradiation position.
 7. A frequency modulation apparatus according toclaim 6, wherein the segment to be adjusted is the last segment for eachof the blocks of the segments.
 8. A frequency modulation apparatusaccording to claim 6, wherein, for each of the blocks, the same value isset for the segment(s) to be adjusted.
 9. A frequency modulationapparatus according to claim 6, wherein an inflection point along anf-θlens characteristic curve is employed to separate the segments intothe blocks.
 10. A frequency modulation apparatus according to claim 1,wherein the laser beam is formed of plural laser beams; and wherein thereference value storing device includes a variable-magnificationcoefficient value generating device for holding a reference value usedas a variable-magnification coefficient for one of the plural laserbeams, and for employing the reference value and a correctioncoefficient corresponding to another laser beam to generate a value thatis used as a variable-magnification coefficient for said another laserbeam.
 11. A frequency modulation apparatus according to claim 10,wherein the correction coefficient for said another laser beam is heldin advance.
 12. A frequency modulation apparatus according to claim 10,further comprising: a storing device for storing a plurality ofcorrection coefficients; and a selecting device for selecting, fromamong the correction coefficients stored in the storing device, acorrection coefficient that corresponds to said another laser beam. 13.A frequency modulation apparatus according to claim 10, wherein aplurality of reference values are held in the holding device, and fromamong the reference values, a reference value is selected as avariable-magnification coefficient for said another laser beam.
 14. Afrequency modulation apparatus according to claim 10, wherein thevariable-magnification coefficient value generating device generates avalue used as a variable-magnification coefficient for said anotherlaser beam by using one or more of a method for adding, to the referencevalue, a predetermined value corresponding to the correctioncoefficient, or for subtracting the predetermined value from thereference value, a method for multiplying the reference value by apredetermined value corresponding to the correction coefficient, amethod for shifting the reference value to the left or right in a mainscan direction by a distance equivalent to a predetermined value thatcorresponds to the correction coefficient, and a method wherebymagnification adjustment in consonance with the correction coefficientis performed for the reference value in the direction leading toward acorrection position, centering on the middle of the optical system. 15.A frequency modulation method, for a frequency modulation apparatus thatincludes a segmentalizing device for dividing, into a plurality ofsegments in units of pixel, a main scan line on an image bearing memberscanned by a laser beam, an auxiliary clock calculation device foremploying a reference clock period, and variable-magnificationcoefficients corresponding to the respective segments, to calculateauxiliary clock periods for the respective segments, and an image clockgenerating device for generating image clocks for the respectivesegments based on an initial predesignated period value and theauxiliary clock periods for the respective segments, comprising: a scandistance measuring step of reading a reference image, and measuring adistance between target images that correspond to the segment in thereference image that has been read; an error ratio calculating step ofcalculating an error ratio of a predesignated reference value to theobtained distance between the target images; and avariable-magnification coefficient changing step of, in accordance withthe obtained error ratio, changing a variable-magnification coefficientof corresponding segment.